Propagation of L1L^{1} and L∞L^{\infty} Maxwellian weighted bounds for derivatives of solutions to the homogeneous elastic Boltzmann Equation

We consider the $n$-dimensional space homogeneous Boltzmann equation for elastic collisions for variable hard potentials with Grad (angular) cutoff. We prove sharp moment inequalities, the propagation of $L^1$-Maxwellian weighted estimates, and consequently, the propagation $L^\infty$-Maxwellian weighted estimates to all derivatives of the initial value problem associated to the afore mentioned problem. More specifically, we extend to all derivatives of the initial value problem associated to this class of Boltzmann equations corresponding sharp moment (Povzner) inequalities and time propagation of $L^1$-Maxwellian weighted estimates as originally developed A.V. Bobylev in the case of hard spheres in 3 dimensions; an improved sharp moments inequalities to a larger class of angular cross sections and $L^1$-exponential bounds in the case of stationary states to Boltzmann equations for inelastic interaction problems with `heating' sources, by A.V. Bobylev, I.M. Gamba and V.Panferov, where high energy tail decay rates depend on the inelasticity coefficient and the the type of `heating' source; and more recently, extended to variable hard potentials with angular cutoff by I.M. Gamba, V. Panferov and C. Villani in the elastic case collision case and so $L^1$-Maxwellian weighted estimated were shown to propagate if initial states have such property. In addition, we also extend to all derivatives the propagation of $L^\infty$-Maxwellian weighted estimates to solutions of the initial value problem to the Boltzmann equations for elastic collisions for variable hard potentials with Grad (angular) cutoff.Comment: 24 page

Soliton structures in a molecular chain model with saturation

In the present work, we study, by means of a one-dimensional lattice model, the collective excitations corresponding to intra molecular ones of a chain like proteins. It is shown that such excitations are described by the Nonlinear Schrodinger equation with saturation. The solutions obtained here are the bell solitons, bubbles, kinks and crowdons. Since they belong to different sectors on the parametric space, the bubble condensation could give place to some important changes of face in this kind of nonlinear system. Additionally, it is shown that the limiting velocity of the solitons is the velocity of sound waves corresponding to longitudinal vibrations of molecules.Comment: 12 pages, 4 figure

Analogue model for anti-de Sitter as a description of point sources in fluids

We introduce an analogue model for a nonglobally hyperbolic spacetime in terms of a two-dimensional fluid. This is done by considering the propagation of sound waves in a radial flow with constant velocity. We show that the equation of motion satisfied by sound waves is the wave equation on $AdS_2\times S^1$. Since this spacetime is not globally hyperbolic, the dynamics of the Klein-Gordon field is not well defined until boundary conditions at the spatial boundary of $AdS_2$ are prescribed. On the analogue model end, those extra boundary conditions provide an effective description of the point source at $r=0$. For waves with circular symmetry, we relate the different physical evolutions to the phase difference between ingoing and outgoing scattered waves. We also show that the fluid configuration can be stable or unstable depending on the chosen boundary condition.Comment: 6 pages, 1 figure. To appear in Phys Rev

Analogue gravity and radial fluid flows: The case of AdS and its deformations

An analogue model for the $\text{AdS}_2$ spacetime has been recently introduced by Mosna, Pitelli and Richartz [Phys. Rev. D 94, 104065 (2016)] by considering sound waves propagating on a fluid with an ill-defined velocity profile at its source/sink. The wave propagation is then uniquely defined only when one imposes an extra boundary condition at the source/sink (which corresponds to the spatial infinity of $\text{AdS}_2$). Here we show that, once this velocity profile is smoothed out at the source/sink, the need for extra boundary conditions disappears. This, in turn, corresponds to deformations of the $\text{AdS}_2$ spacetime near its spatial infinity. We also examine how this regularization of the velocity profile picks up a specific boundary condition for the idealized system, so that both models agree in the long wavelength limit.Comment: 6 pages, 3 figures. To appear in Phys Rev

Healthcare workers in Saudi Arabia (KSA) perceive stress differently according to gender but not in cortisol levels - an immunoassay study

Background: Working in the healthcare sector is generally regarded as stress inductive, which hampers performance, yet one demanding constant accuracy. This dichotomy has led to numerous investigations on the impact from perceived stress on hospital workers but focused primarily on employing psychological methods to determine perceived stress. This study sought to employ an arguably more objective measure of chronic stress on female healthcare professionals in Saudi Arabia, by assaying the concentration of hair cortisol (HCC) in parallel with stress questionnaires. Methods: Pharmacists, nurses and lab workers participated in providing hair samples. Cortisol levels were subsequently quantified using immunoassay methods. Investigations considered the variables of age, gender, and smoking, hair coloring or bleaching or working in shifts on both stress perception and HCC. Results: On average chronic stress was perceived comparably between the different healthcare professions and not differ significantly against the female control group. However, chronic stress differed significantly between genders within the healthcare profession. In contrast, HCC levels showed no direct relation to stress perception with respect to either gender or profession. HCC did, however, show steady decreases with respect to age, as an indirect measure of experience, that contrasted against the identical scores for stress perception. Finally, night shifts, smoking or hair colouring did not produce a significant change on HCC in the healthcare cohorts. Conclusions: Women in the healthcare profession perceive stress higher irrespective of profession compared to men. Also show a pattern of decreasing levels of cortisol with increasing age despite reporting similar stress perception against younger participants